A and B; and A, B are the harmonic conjugates of P, Q. Prop. 23. To divide a given straight line internallyand externally so that the segments may he in a givenratio, i.e., to divide a given straight line harmonically. Let AB be the given straight line, and a : h thegiven ratio. Through A and B… … AP AO Hence ^^5 = ^* iiil AB if^ divided luu-mouically.PB QB If three collinear points, A, P, B, he given, thentaking AX = AP and BY = BY-=PB, and eonstrnoting asin the proposition, a fourth point Q is found sueh thatA, P, B, Q form a harmonic range. It is important to observe that the solution is…
Geometry · Geometry, Plane
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